The Human Lumbar Spine During High-Rate Under Seat Loading: A Combined Metric Injury Criteria.

Modern changes in warfare have shown an increased incidence of lumbar spine injuries caused by underbody blast events. The susceptibility of the lumbar spine during these scenarios could be exacerbated by coupled moments that act with the rapid compressive force depending on the occupant's seated posture. In this study, a combined loading lumbar spine vertebral body fracture injury criteria (Lic) across a range of postures was established from 75 tests performed on instrumented cadaveric lumbar spine specimens. The spines were predominantly exposed to axial compressive forces from an upward vertical thrust with 64 of the tests resulting in at least one vertebral body fracture and 11 in no vertebral body injury. The proposed Lic utilizes a recommended metric (κ), based on prismatic beam failure theory, resulting from the combination of the T12-L1 resultant sagittal force and the decorrelated bending moment with optimized critical values of Fr,crit = 5824 N and My,crit = 1155 Nm. The 50% risk of lumbar spine injury corresponded to a combined metric of 1, with the risk decreasing with the combined metric value. At 50% injury risk the Normalized Confidence Interval Size improved from 0.24 of a force-based injury reference curve to 0.17 for the combined loading metric.

Specimen-specific fracture risk curves of lumbar vertebrae under dynamic axial compression.

Underbody blast attacks of military vehicles by improvised explosives have resulted in high incidence of lumbar spine fractures below the thorocolumbar junction in military combatants. Fracture risk curves related to vertical loading at individual lumbar spinal levels can be used to assess the protective ability of new injury mitigation equipment. The objectives of this study were to derive fracture risk curves for the lumbar spine under high rate compression and identify how specimen-specific attributes and lumbar spinal level may influence fracture risk. In this study, we tested a sample of three-vertebra specimens encompassing all spinal levels between T12 to S1 in high-rate axial compression. Each specimen was tested with a non-injurious load, followed by a compressive force sufficient to induce vertebral body fracture. During testing, bone fracture was identified using measurements from acoustic emission sensors and changes in load cell readings. Following testing, the fractures were assessed using computed tomographic (CT) imaging. The CT images showed isolated fractures of trabecular bone, or fractures involving both cortical and trabecular bone. Results from the compressive force measurements in conjunction with a survival analysis demonstrated that the compressive force corresponding to fracture increased inferiorly as a function of lumbar spinal level. The axial rigidity (EA) measured at the mid-plane of the centre vertebra or the volumetric bone mineral density (vBMD) of the vertebral body trabecular bone most greatly influenced fracture risk. By including these covariates in the fracture risk curves, no other variables significantly affected fracture risk, including the lumbar spinal level. The fracture risk curves presented in this study may be used to assess the risk of injury at individual lumbar vertebra when exposed to dynamic axial compression.

Human Lumbar Spine Responses from Vertical Loading: Ranking of Forces Via Brier Score Metrics and Injury Risk Curves.

This study was conducted to quantify the human tolerance from inferior to superior impacts to whole lumbar spinal columns excised from 43 post mortem human subjects. The specimens were fixed at the ends, aligned in a consistent seated posture, load cells were attached to the proximal and distal ends of the fixation, and the impact was applied using a custom accelerator device. Pretest X-rays and computed tomography (CT) scans, prepositioned X-rays, and posttest X-rays, CT scans and dissection data were used to identify injuries. Right, left, and interval censoring processes were used for the survival analysis, 16 were right censored, 24 were interval censored, and three were left censored observations. Force-based injury risk curves were developed, and the optimal metric describing the underlying response to injury was identified using the Brier score metric. Material, geometry (disc and body areas), and demographic covariates were included in the analysis. The distal force was found to be optimal metric. The bone mineral density was a significant covariate for distal and proximal forces. Both material and geometrical factors affected the transmitted force in this mode of loading. These quantified data serve as the first set of human lumbar spinal column injury risk curves.

Cortical and Trabecular Bone Fracture Characterisation in the Vertebral Body Using Acoustic Emission.

The ability to rapidly detect localised fractures of cortical and/or trabecular bone sustained by the vertebral body would enhance the analysis of vertebral fracture initiation and propagation during dynamic loading. In this study, high rate axial compression tests were performed on twenty sets of three-vertebra lumbar spine specimens. Acoustic Emission (AE) sensor measurements of sound wave pressure were used to classify isolated trabecular fractures and severe compressive fractures of vertebral body cortical and trabecular bone. Fracture detection using standard AE parameters was compared to that of traditional mechanical parameters obtained from load cell and displacement readings. Results indicated that the AE parameters achieved slightly enhanced classification of isolated trabecular fractures, whereas the mechanical parameters better identified combined fractures of cortical and trabecular bone. These findings demonstrate that AE may be used to promptly and accurately identify localised fractures of trabecular bone, whereas more extensive fractures of the vertebral body are best identified by load cell readings due to the considerable loss in compressive resistance. The discrimination thresholds corresponding to the AE parameters were based on calibrated measurements of AE wave pressure and may ultimately be used to examine the onset and progression of vertebral fracture in other loading scenarios.

Role of disc area and trabecular bone density on lumbar spinal column fracture risk curves under vertical impact.

While studies have been conducted using human cadaver lumbar spines to understand injury biomechanics in terms of stability/energy to fracture, and physiological responses under pure-moment/follower loads, data are sparse for inferior-to-superior impacts. Injuries occur under this mode from underbody blasts. OBJECTIVES: determine role of age, disc area, and trabecular bone density on tolerances/risk curves under vertical loading from a controlled group of specimens. T12-S1 columns were obtained, pretest X-rays and CTs taken, load cells attached to both ends, impacts applied at S1-end using custom vertical accelerator device, and posttest X-ray, CT, and dissections done. BMD of L2-L4 vertebrae were obtained from QCT. Survival analysis-based Human Injury Probability Curves (HIPCs) were derived using proximal and distal forces. Age, area, and BMD were covariates. Forces were considered uncensored, representing the load carrying capacity. The Akaike Information Criterion was used to determine optimal distributions. The mean forces, ±95% confidence intervals, and Normalized Confidence Interval Size (NCIS) were computed. The Lognormal distribution was the optimal function for both forces. Age, area, and BMD were not significant (p > 0.05) covariates for distal forces, while only BMD was significant for proximal forces. The NCIS was the lowest for force-BMD covariate HIPC. The HIPCs for both genders at 35 and 45 years were based on population BMDs. These HIPCs serve as human tolerance criteria for automotive, military, and other applications. In this controlled group of samples, BMD is a better predictor-covariate that characterizes lumbar column injury under inferior-to-superior impacts.

Effect of lamellarity and size on calorimetric phase transitions in single component phosphatidylcholine vesicles.

Nano-differential scanning calorimetry (nano-DSC) is a powerful tool in the investigation of unilamellar (small unilamellar, SUVs, or large unilamellar, LUVs) vesicles, as well as lipids on supported bilayers, since it measures the main gel-to-liquid phase transition temperature (Tm), enthalpies and entropies. In order to assign these transitions in single component systems, where Tm often occurred as a doublet, nano-DSC, dynamic light scattering and cryo-transmission electron microscopy (cryo-TEM) data were compared. The two Tms were not attributable to decoupled phase transitions between the two leaflets of the bilayer, i.e. nano-DSC measurements were not able to distinguish between the outer and inner leaflets of the vesicle bilayers. Instead, the two Tms were attributed to mixtures of oligolamellar and unilamellar vesicles, as confirmed by cryo-TEM images. Tm for the oligolamellar vesicles was assigned to the peak closest to that of the parent multilamellar vesicle (MLV) peak. The other transition was higher than that of the parent MLVs for 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC), and increased in temperature as the vesicle size decreased, while it was lower in temperature than that of the parent MLVs for 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC), and decreased as the vesicle size decreased. These subtle shifts arose due to small differences in the values of ΔH and ΔS, since Tm is determined by their ratio (ΔH/ΔS). It was not possible to completely eliminate oligolamellar structures for MLVs extruded with the 200 nm pore size filter, even after 120 passes, while these structures were eliminated for MLVs extruded through the 50 nm pore size filter.

Methodology to determine skull bone and brain responses from ballistic helmet-to-head contact loading using experiments and finite element analysis.

The objective of the study was to obtain helmet-to-head contact forces from experiments, use a human head finite element model to determine regional responses, and compare outputs to skull fracture and brain injury thresholds. Tests were conducted using two types of helmets (A and B) fitted to a head-form. Seven load cells were used on the head-form back face to measure helmet-to-head contact forces. Projectiles were fired in frontal, left, right, and rear directions. Three tests were conducted with each helmet in each direction. Individual and summated force- and impulse-histories were obtained. Force-histories were inputted to the human head-helmet finite element model. Pulse durations were approximately 4 ms. One-third force and impulse were from the central load cell. 0.2% strain and 40 MPa stress limits were not exceeded for helmet-A. For helmet-B, strains exceeded in left, right, and rear; pressures exceeded in bilateral directions; volume of elements exceeding 0.2% strains correlated with the central load cell forces. For helmet-A, volumes exceeding brain pressure threshold were: 5-93%. All elements crossed the pressure limit for helmet-B. For both helmets, no brain elements exceeded peak principal strain limit. These findings advance our understanding of skull and brain biomechanics from helmet-head contact forces.

Method for obtaining simple shear material properties of the intervertebral disc under high strain rates.

Predicting spinal injury under high rates of vertical loading is of interest, but the success of computational models in modeling this type of loading scenario is highly dependent on the material models employed. Understanding the response of these biological materials at high strain rates is critical to accurately model mechanical response of tissue and predict injury. While data exists at lower strain rates, there is a lack of the high strain rate material data that are needed to develop constitutive models. The Split Hopkinson Pressure Bar (SHPB) has been used for many years to obtain properties of various materials at high strain rates. However, this apparatus has mainly been used for characterizing metals and ceramics and is difficult to apply to softer materials such as biological tissue. Recently, studies have shown that modifications to the traditional SHPB setup allow for the successful characterization of mechanical properties of biological materials at strain rates and peak strain values that exceed alternate soft tissue testing techniques. In this paper, the previously-reported modified SHPB technique is applied to characterize human intervertebral disc material under simple shear. The strain rates achieved range from 5 to 250 strain s-1. The results demonstrate the sensitivity to the disc composition and structure, with the nucleus pulposus and annulus fibrosus exhibiting different behavior under shear loading. Shear tangent moduli are approximated at varying strain levels from 5 to 20% strain. This data and technique facilitates determination of mechanical properties of intervertebral disc materials under shear loading, for eventual use in constitutive models.

Effects of tissue preservation temperature on high strain-rate material properties of brain.

Postmortem preservation conditions may be one of factors contributing to wide material property variations in brain tissues in literature. The objective of present study was to determine the effects of preservation temperatures on high strain-rate material properties of brain tissues using the split Hopkinson pressure bar (SHPB). Porcine brains were harvested immediately after sacrifice, sliced into 2 mm thickness, preserved in ice cold (group A, 10 samples) and 37°C (group B, 9 samples) saline solution and warmed to 37°C just prior to the test. A SHPB with tube aluminum transmission bar and semi-conductor strain gauges were used to enhance transmitted wave signals. Data were gathered using a digital acquisition system and processed to obtain stress-strain curves. All tests were conducted within 4 h postmortem. The mean strain-rate was 2487±72 s(-1). A repeated measures model with specimen-level random effects was used to analyze log transformed stress-strain responses through the entire loading range. The mean stress-strain curves with ±95% confidence bands demonstrated typical power relationships with the power value of 2.4519 (standard error, 0.0436) for group A and 2.2657 (standard error, 0.0443) for group B, indicating that responses for the two groups are significantly different. Stresses and tangent moduli rose with increasing strain levels in both groups. These findings indicate that storage temperatures affected brain tissue material properties and preserving tissues at 37°C produced a stiffer response at high strain-rates. Therefore, it is necessary to incorporate material properties obtained from appropriately preserved tissues to accurately predict the responses of brain using stress analyses models, such as finite element simulations.

Physical properties of the human head: mass, center of gravity and moment of inertia.

This paper presents a synthesis of biomedical investigations of the human head with specific reference to certain aspects of physical properties and development of anthropometry data, leading to the advancement of dummies used in crashworthiness research. As a significant majority of the studies have been summarized as reports, an effort has been made to chronologically review the literature with the above objectives. The first part is devoted to early studies wherein the mass, center of gravity (CG), and moment of inertia (MOI) properties are obtained from human cadaver experiments. Unembalmed and preserved whole-body and isolated head and head-neck experiments are discussed. Acknowledging that the current version of the Hybrid III dummy is the most widely used anthropomorphic test device in motor vehicle crashworthiness research for frontal impact applications for over 30 years, bases for the mass and MOI-related data used in the dummy are discussed. Since the development and federalization of the dummy in the United States, description of methods used to arrive at these properties form a part of the manuscript. Studies subsequent to the development of this dummy including those from the US Military are also discussed. As the head and neck are coupled in any impact, and increasing improvements in technology such as advanced airbags, and pre-tensioners and load limiters in manual seatbelts affect the kinetics of the head-neck complex, the manuscript underscores the need to pursue studies to precisely determine all the physical properties of the head. Because the most critical parameters (locations of CG and occipital condyles (OC), mass, and MOI) have not been determined on a specimen-by-specimen basis in any single study, it is important to gather these data in future experiments. These critical data will be of value for improving occupant safety, designing advanced restraint systems, developing second generation dummies, and assessing the injury mitigating characteristics of modern vehicle components in all impact modalities.

A finite element study of blast traumatic brain injury - biomed 2009.

An idealized finite element human head model was constructed to study biomechanical responses in the brain due to blast overpressure loading from a blast of 10 kg TNT at 1 meter. Brain strain in the coup and contrecoup regions were 4-7x higher than the central region, and high brain strain (15%) large deformation (4 mm) occurred in the brainstem region, indicating a higher probability of injury in the peripheral brain and brainstem regions due to blast overpressure loading.

Association of contact loading in diffuse axonal injuries from motor vehicle crashes.

BACKGROUND: Although studies have been conducted to analyze brain injuries from motor vehicle crashes, the association of head contact has not been fully established. This study examined the association in occupants sustaining diffuse axonal injuries (DAIs). METHODS: The 1997 to 2006 motor vehicle Crash Injury Research Engineering Network database was used. All crash modes and all changes in velocity were included; ejections and rollovers were excluded; injuries to front and rear seat occupants with and without restraint use were considered. DAI were coded in the database using Abbreviated Injury Scale 1990. Loss of consciousness was included and head contact was based on medical- and crash-related data. RESULTS: Sixty-seven occupants with varying ages were coded with DAI. Forty-one adult occupants (mean, 33 years of age, 171-cm tall, 71-kg weight; 30 drivers, 11 passengers) were analyzed. Mean change in velocity was 41.2 km/h and Glasgow Coma Scale score was 4. There were 33 lateral, 6 frontal, and 2 rear crashes with 32 survivors and 9 were fatalities. Two occupants in the same crash did not sustain DAI. Although skull fractures and scalp injuries occurred in some impacts, head contact was identified in all frontal, rear, and far side, and all but one nearside crashes. CONCLUSIONS: Using a large sample size of occupants sustaining DAI in 1991 to 2006 model year vehicles, DAI occurred more frequently in side than frontal crashes, is most commonly associated with impact load transfer, and is not always accompanied by skull fractures. The association of head contact in >95% of cases underscores the importance of evaluating crash-related variables and medical information for trauma analysis. It would be prudent to include contact loading in addition to angular kinematics in the analysis and characterization of DAI.

A finite element model of region-specific response for mild diffuse brain injury.

It is well known that rotational loading is responsible for a spectrum of diffuse brain injuries spanning from concussion to diffuse axonal trauma. Many experimental studies have been performed to understand the pathological and biomechanical factors associated with diffuse brain injuries. Finite element models have also been developed to correlate experimental findings with intrinsic variables such as strain. However, a paucity of studies exist examining the combined role of the strain-time parameter. Consequently, using the principles of finite element analysis, the present study introduced the concept of sustained maximum principal strain (SMPS) criterion and explored its potential applicability to diffuse brain injury. An algorithm was developed to determine if the principal strain in a finite element of the brain exceeded a specified magnitude over a specific time interval. The anatomical and geometrical details of the rat for the two-dimensional model were obtained from published data. Using material properties from literature and iterative techniques, the model was validated under three distinct rotational loading conditions indicative of non-injury, concussion, and diffuse axonal trauma. Validation results produced a set of material properties to define the model and were deemed appropriate to examine the role of sustained strain as an indicator of the mechanics of mild diffuse brain injury at the local level. Using a separate set of histological data obtained from graded mild diffuse brain injury experimental studies in rats, different formulations of SMPS criterion were evaluated. For the hippocampus and parietal cortex regions, 4-4 SMPS criterion was found to most closely match with the pattern of histological results. This was further verified by correlating the fractional areas to the time of unconsciousness for each animal group. Although not fully conclusive, these results are valuable in the understanding of diffuse brain injury pathologies following rotational loading.

Experimental study of blast-induced traumatic brain injury using a physical head model.

This study was conducted to quantify intracranial biomechanical responses and external blast overpressures using physical head model to understand the biomechanics of blast traumatic brain injury and to provide experimental data for computer simulation of blast-induced brain trauma. Ellipsoidal-shaped physical head models, made from 3-mm polycarbonate shell filled with Sylgard 527 silicon gel, were used. Six blast tests were conducted in frontal, side, and 45 degrees oblique orientations. External blast overpressures and internal pressures were quantified with ballistic pressure sensors. Blast overpressures, ranging from 129.5 kPa to 769.3 kPa, were generated using a rigid cannon and 1.3 to 3.0 grams of pentaerythritol tetranitrate (PETN) plastic sheet explosive (explosive yield of 13.24 kJ and TNT equivalent mass of 2.87 grams for 3 grams of material). The PETN plastic sheet explosive consisted of 63% PETN powder, 29% plasticizer, and 8% nitrocellulose with a density of 1.48 g/cm3 and detonation velocity of 6.8 km/s. Propagation and reflection of the shockwave was captured using a shadowgraph technique. Shockwave speeds ranging from 423.3 m/s to 680.3 m/s were recorded. The model demonstrated a two-stage response: a pressure dominant (overpressure) stage followed by kinematic dominant (blast wind) stage. Positive pressures in the brain simulant ranged from 75.1 kPa to 1095 kPa, and negative pressures ranged from -43.6 kPa to -646.0 kPa. High- and normal-speed videos did not reveal observable deformations in the brain simulant from the neutral density markers embedded in the midsagittal plane of the head model. Amplitudes of the internal positive and negative pressures were found to linearly correlate with external overpressure. Results from the current study suggested a pressure-dominant brain injury mechanism instead of strain injury mechanism under the blast severity of the current study. These quantitative results also served as the validation and calibration data for computer simulation models of blast brain injuries.

Dynamic biomechanics of the human head in lateral impacts.

The biomechanical responses of human head (translational head CG accelerations, rotational head accelerations, and HIC) under lateral impact to the parietal-temporal region were investigated in the current study. Free drop tests were conducted at impact velocities ranging from 2.44 to 7.70 m/s with a 40 durometer, a 90 durometer flat padding, and a 90 durometer cylinder. Specimens were isolated from PMHS subjects at the level of occipital condyles, and the intracranial substance was replaced with brain simulant (Sylgard 527). Three tri-axial accelerometers were instrumented at the anterior, posterior, and vertex of the specimen, and a pyramid nine accelerometer package (pNAP) was used at the contra-lateral site. Biomechanical responses were computed by transforming accelerations measured at each location to the head CG. The results indicated significant "hoop effect" from skull deformation. Translational head CG accelerations were accurately measured by transforming the pNAP, the vertex accelerations, or the average of anterior/posterior acceleration to the CG. The material stiffness and structural rigidity of the padding changed the biomechanical responses of the head with stiffer padding resulting in higher head accelerations. At the skull fracture, HIC values were more than 2-3x higher than the frontal skull fracture threshold (HIC=1000), emphasizing the differences between frontal and lateral impact. Rotational head accelerations up to 42.1 krad/s(2) were observed before skull fracture, indicating possible severe brain injury without skull fracture in lateral head impact. These data will help to establish injury criteria and threshold in lateral impacts for improved automotive protection and help clinicians understand the biomechanics of lateral head impact from improved diagnosis.

Influence of angular acceleration-deceleration pulse shapes on regional brain strains.

Recognizing the association of angular loading with brain injuries and inconsistency in previous studies in the application of the biphasic loads to animal, physical, and experimental models, the present study examined the role of the acceleration-deceleration pulse shapes on region-specific strains. An experimentally validated two-dimensional finite element model representing the adult male human head was used. The model simulated the skull and falx as a linear elastic material, cerebrospinal fluid as a hydrodynamic material, and cerebrum as a linear viscoelastic material. The angular loading matrix consisted coronal plane rotation about a center of rotation that was acceleration-only (4.5 ms duration, 7.8 krad/s/s peak), deceleration-only (20 ms, 1.4 krad/s/s peak), acceleration-deceleration, and deceleration-acceleration pulses. Both biphasic pulses had peaks separated by intervals ranging from 0 to 25 ms. Principal strains were determined at the corpus callosum, base of the postcentral sulcus, and cerebral cortex of the parietal lobe. The cerebrum was divided into 17 regions and peak values of average maximum principal strains were determined. In all simulations, the corpus callosum responded with the highest strains. Strains were the least under all simulations in the lower parietal lobes. In all regions peak strains were the same for both monophase pulses suggesting that the angular velocity may be a better metric than peak acceleration or deceleration. In contrast, for the biphasic pulse, peak strains were region- and pulse-shape specific. Peak values were lower in both biphasic pulses when there was no time separation between the pulses than the corresponding monophase pulse. Increasing separation time intervals increased strains, albeit non-uniformly. Acceleration followed by deceleration pulse produced greater strains in all regions than the other form of biphasic pulse. Thus, pulse shape appears to have an effect on regional strains in the brain.

Upper neck forces and moments and cranial angular accelerations in lateral impact.

Biomechanical studies using postmortem human subjects (PMHS) in lateral impact have focused primarily on chest and pelvis injuries, mechanisms, tolerances, and comparison with side impact dummies. A paucity of data exists on the head-neck junction, i.e., forces and moments, and cranial angular accelerations. The objective of this study was to determine lateral impact-induced three-dimensional temporal forces and moments at the head-neck junction and cranial linear and angular accelerations from sled tests using PMHS and compare with responses obtained from an anthropomorphic test device (dummy) designed for lateral impact. Following initial evaluations, PMHS were seated on a sled, restrained using belts, and lateral acceleration was applied. Specimens were instrumented with a pyramid-shaped nine-accelerometer package to record cranial accelerations. A sled accelerometer was used to record the input acceleration. Radiographs and computed tomography scans were obtained to identify pathology. A similar testing protocol was adopted for dummy tests. Results indicated that profiles of forces and moments at the head-neck junction and cranial accelerations were similar between the two models. However, peak forces and moments at the head-neck junction were lower in the dummy than PMHS. Peak cranial linear and angular accelerations were also lower in the dummy than in the PMHS. Fractures to the head-neck complex were not identified in PMHS tests. Peak cranial angular accelerations were suggestive of mild traumatic brain injury with potential for loss of consciousness. Findings from this study with a limited dataset are valuable in establishing response corridors for side impacts and evaluating side impact dummies used in crashworthiness and safety-engineering studies.

How to test brain and brain simulant at ballistic and blast strain rates.

Mechanical properties of brain tissue and brain simulant at strain rate in the range of 1000 s-1 are essential for computational simulation of intracranial responses for ballistic and blast traumatic brain injury. Testing these ultra-soft materials at high strain rates is a challenge to most conventional material testing methods. The current study developed a modified split Hopkinson bar techniques using the combination of a few improvements to conventional split Hopkinson bar including: using low impedance aluminum bar, semiconductor strain gauge, pulse shaping technique and annular specimen. Feasibility tests were conducted using a brain stimulant, Sylgard 527. Stress-strain curves of the simulant were successfully obtained at strain rates of 2600 and 2700 s-1 for strain levels up to 60%. This confirmed the applicability of Hopkinson bar for mechanical properties testing of brain tissue in the ballistic and blast domain.

Regional brain strains and role of falx in lateral impact-induced head rotational acceleration.

The objective of the present investigation is to determine localized brains strains in lateral impact using finite element modeling and evaluate the role of the falx. A two-dimensional finite element model was developed and validated with experimental data from literature. Motions and strains from the stress analysis matched well with experimental results. A parametric study was conducted by introducing flexible falx in the finite element model. For the model with the rigid falx, high strains were concentrated in the corpus callosum, whereas for the model with the flexible falx, high strains extended into the cerebral vertex. These preliminary findings indicate that the flexibility of falx has an effect on regional brain strains in lateral impact.